Another operation on matrices is scalar multiplication. Let k be a real number and A = [ a...

Another operation on matrices is scalar multiplication. Let k be a real number and A = [ aij ]be an m × n matrix. The result of multiplying A by the scalar k is the matrix kA = [ kaij ]. For Exercises, use the definition of scalar multiplication and the matrices given.

,  and

Exercise

Show that scalar multiplication has the following property.

k (A + B) = k A + k B